|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.479 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.165 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.981 |
|
|
\[
{}y^{\prime }+y = \frac {1}{x}
\] |
[[_linear, ‘class A‘]] |
✗ |
0.216 |
|
|
\[
{}y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_linear, ‘class A‘]] |
✗ |
0.237 |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
0.427 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✗ |
0.134 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{x}
\] |
[[_2nd_order, _quadrature]] |
✗ |
0.056 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{x}
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.065 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.060 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.062 |
|
|
\[
{}h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2}
\] |
[_quadrature] |
✓ |
2.345 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (x +2\right ) {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.750 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.389 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{a \cos \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.949 |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.395 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.894 |
|
|
\[
{}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0
\] |
[_separable] |
✓ |
1.130 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
14.723 |
|
|
\[
{}y^{\prime } = \frac {y x +3 x -2 y+6}{y x -3 x -2 y+6}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.812 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.338 |
|
|
\[
{}y^{\prime } = a
\] |
[_quadrature] |
✓ |
0.313 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.214 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.411 |
|
|
\[
{}y^{\prime } = a x
\] |
[_quadrature] |
✓ |
0.147 |
|
|
\[
{}y^{\prime } = a x y
\] |
[_separable] |
✓ |
0.799 |
|
|
\[
{}y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.657 |
|
|
\[
{}y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.781 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.439 |
|
|
\[
{}y^{\prime } = b y
\] |
[_quadrature] |
✓ |
0.392 |
|
|
\[
{}y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.031 |
|
|
\[
{}c y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.339 |
|
|
\[
{}c y^{\prime } = a
\] |
[_quadrature] |
✓ |
0.319 |
|
|
\[
{}c y^{\prime } = a x
\] |
[_quadrature] |
✓ |
0.184 |
|
|
\[
{}c y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.720 |
|
|
\[
{}c y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.791 |
|
|
\[
{}c y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.540 |
|
|
\[
{}c y^{\prime } = b y
\] |
[_quadrature] |
✓ |
0.579 |
|
|
\[
{}c y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.173 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r}
\] |
[[_Riccati, _special]] |
✓ |
1.237 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r x}
\] |
[_rational, _Riccati] |
✓ |
3.790 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}}
\] |
[_rational, _Riccati] |
✓ |
5.656 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{y}
\] |
[_rational, _Bernoulli] |
✓ |
1.492 |
|
|
\[
{}a \sin \left (x \right ) y x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.376 |
|
|
\[
{}f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi = 0
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.162 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y^{2}
\] |
[_Riccati] |
✓ |
2.267 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y}{x}
\] |
[_linear] |
✓ |
1.122 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y^{2}}{x}
\] |
[_Riccati] |
✗ |
3.011 |
|
|
\[
{}y^{\prime } = x +y+b y^{2}
\] |
[_Riccati] |
✓ |
1.110 |
|
|
\[
{}y^{\prime } x = 0
\] |
[_quadrature] |
✓ |
0.338 |
|
|
\[
{}5 y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.336 |
|
|
\[
{}{\mathrm e} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.358 |
|
|
\[
{}\pi y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.355 |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.387 |
|
|
\[
{}f \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.375 |
|
|
\[
{}y^{\prime } x = 1
\] |
[_quadrature] |
✓ |
0.260 |
|
|
\[
{}y^{\prime } x = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}\left (x -1\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.342 |
|
|
\[
{}y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.335 |
|
|
\[
{}x y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.337 |
|
|
\[
{}x y \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.336 |
|
|
\[
{}\pi y \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.341 |
|
|
\[
{}x \sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.394 |
|
|
\[
{}x \sin \left (x \right ) {y^{\prime }}^{2} = 0
\] |
[_quadrature] |
✓ |
0.137 |
|
|
\[
{}y {y^{\prime }}^{2} = 0
\] |
[_quadrature] |
✓ |
0.127 |
|
|
\[
{}{y^{\prime }}^{n} = 0
\] |
[_quadrature] |
✓ |
0.386 |
|
|
\[
{}x {y^{\prime }}^{n} = 0
\] |
[_quadrature] |
✓ |
0.347 |
|
|
\[
{}{y^{\prime }}^{2} = x
\] |
[_quadrature] |
✓ |
0.175 |
|
|
\[
{}{y^{\prime }}^{2} = x +y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.392 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.360 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{2}}{x}
\] |
[_separable] |
✓ |
1.135 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.747 |
|
|
\[
{}{y^{\prime }}^{3} = \frac {y^{2}}{x}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.029 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{y x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.587 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.647 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x^{2} y^{3}}
\] |
[_separable] |
✓ |
0.661 |
|
|
\[
{}{y^{\prime }}^{4} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.007 |
|
|
\[
{}{y^{\prime }}^{2} = \frac {1}{x^{3} y^{4}}
\] |
[_separable] |
✓ |
0.806 |
|
|
\[
{}y^{\prime } = \sqrt {1+6 x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.340 |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.687 |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.573 |
|
|
\[
{}y^{\prime } = \left (a +b x +y\right )^{4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
156.417 |
|
|
\[
{}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
17.291 |
|
|
\[
{}y^{\prime } = \left (a +b x +c y\right )^{6}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.695 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
1.757 |
|
|
\[
{}y^{\prime } = 10+{\mathrm e}^{x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.792 |
|
|
\[
{}y^{\prime } = 10 \,{\mathrm e}^{x +y}+x^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.582 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x +y}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.060 |
|
|
\[
{}y^{\prime } = 5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.198 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.169 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.911 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.265 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.150 |
|
|
\[
{}{y^{\prime \prime }}^{2} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.215 |
|
|
\[
{}{y^{\prime \prime }}^{n} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.128 |
|
|
\[
{}a y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.164 |
|
|
\[
{}a {y^{\prime \prime }}^{2} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.205 |
|
|
\[
{}a {y^{\prime \prime }}^{n} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.481 |
|